Unit 1
Review of mathematical preliminaries: Vector – Function space – Basis function – Review of fourier theory and properties of fourier transform – Short time fourier transform – Heisenberg’s uncertainty principle – Continuous wavelet transform – CWT and its Properties – DWT – Time-frequency tiling
Unit 2
Discrete Wavelet Transform – Haar scaling function – Nested spaces – Wavelet function. Designing orthogonal wavelet systems: Daubechies – Coiflet – Symlet wavelet system coefficients – Signal decomposition using DWT – Relation to filter banks and frequency response – Signal reconstruction using DWT – M band wavelets.